Maximizing Index Diversity in Committee Elections

Paula Böhm, Robert Bredereck, Till Fluschnik

Keywords: labeled multiwinner elections, axiomatic characterization, computational complexity

TL;DR: We present 2 models for selecting diverse committees in multiwinner elections, balancing diversity with either a minimum score or voter satisfaction, and examine different diversity indices, their axiomatic properties, and computational complexity.

Abstract: We introduce two models of multiwinner elections with approval preferences and labelled candidates that take the committee's diversity into account. One model aims to find a committee with maximal diversity given a scoring function (e.g. of a scoring-based voting rule) and a lower bound for the score to be respected. The second model seeks to maximize the diversity given a minimal satisfaction for each agent to be respected. To measure the diversity of a committee, we use multiple diversity indices used in ecology and introduce one new index. We define (desirable) properties of diversity indices, test the indices considered against these properties, and characterize the new index. We analyze the computational complexity of computing a committee for both models with most of the indices considered and scoring functions of well-known voting rules, and investigate the influence of weakening the score or satisfaction constraints on the diversity empirically.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1061